SharePoint Lookup Columns and Projected fields are great way to build relationships between various lists.
However, there is a small limitation: You cannot lookup on Choice Columns, Lookups to other lists columns.
For e.g. I can establish a relationship to Title (Single Line of Text) Column, but not to Status (Choice) Column in my primary list.
On the Created Column UI, after you select the list, they are not listed in the dropdow to select the column (In this column:). They are also missing from the project fields check boxes (Add a column to show each of these additional fields:)
Quick Cheat Sheet: Created a Calculated Column in the Master List referring your original Choice Column.
SharePoint allows Calculated Columns to be used as Lookup Columns or Projected Fields in your Child List.